Skip to main content
SpringerLink
Log in

Hierarchical Attribute-Based Signatures: Short Keys and Optimal Signature Length

  • Conference paper
  • First Online:
Book cover Applied Cryptography and Network Security (ACNS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11464))

Included in the following conference series:

Abstract

With Attribute-based Signatures (ABS) users can simultaneously sign messages and prove compliance of their attributes, issued by designated attribute authorities, with some verification policy. Neither signer’s identity nor possessed attributes are leaked during the verification process, making ABS schemes a handy tool for applications requiring privacy-preserving authentication. Earlier ABS schemes lacked support for hierarchical delegation of attributes (across tiers of attribute authorities down to the signers), a distinct property that has made traditional PKIs more scalable and widely adoptable.

This changed recently with the introduction of Hierarchical ABS (HABS) schemes, where support for attribute delegation was proposed in combination with stronger privacy guarantees for the delegation paths (path anonymity) and new accountability mechanisms allowing a dedicated tracing authority to identify these paths (path traceability) and the signer, along with delegated attributes, if needed. Yet, current HABS construction is generic with inefficient delegation process resulting in sub-optimal signature lengths of order \(O(k^{2}|\varPsi |)\) where \(\varPsi \) is the policy size and k the height of the hierarchy.

This paper proposes a direct HABS construction in bilinear groups that significantly improves on these bounds and satisfies the original security and privacy requirements. At the core of our HABS scheme is a new delegation process based on the length-reducing homomorphic trapdoor commitments to group elements for which we introduce a new delegation technique allowing step-wise commitments to additional elements without changing the length of the original commitment and its opening. While also being of independent interest, this technique results in shorter HABS keys and achieves the signature-length growth of \(O(k|\varPsi |)\) which is optimal due to the path-traceability requirement.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abe, M., Chase, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Constant-size structure-preserving signatures: generic constructions and simple assumptions. J. Cryptol. 29, 833–878 (2016)

    Google Scholar 

  2. Abe, M., Haralambiev, K., Ohkubo, M.: Signing on elements in bilinear groups for modular protocol design. IACR Cryptology ePrint Archive, p. 133 (2010)

    Google Scholar 

  3. Backes, M., Meiser, S., Schröder, D.: Delegatable functional signatures. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 357–386. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_14

    Chapter  Google Scholar 

  4. Belenkiy, M., Camenisch, J., Chase, M., Kohlweiss, M., Lysyanskaya, A., Shacham, H.: Randomizable proofs and delegatable anonymous credentials. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 108–125. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_7

    Chapter  Google Scholar 

  5. Bellare, M., Fuchsbauer, G.: Policy-based signatures. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 520–537. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_30

    Chapter  Google Scholar 

  6. Blazy, O., Fuchsbauer, G., Izabachène, M., Jambert, A., Sibert, H., Vergnaud, D.: Batch Groth–Sahai. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 218–235. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13708-2_14

    Chapter  Google Scholar 

  7. Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_4

    Chapter  Google Scholar 

  8. Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_29

    Chapter  Google Scholar 

  9. Camenisch, J., Lysyanskaya, A.: A signature scheme with efficient protocols. In: Cimato, S., Persiano, G., Galdi, C. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36413-7_20

    Chapter  Google Scholar 

  10. Chaum, D.: Security without identification: transaction systems to make big brother obsolete. Commun. ACM 28(10), 1030–1044 (1985)

    Article  Google Scholar 

  11. Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_22

    Chapter  Google Scholar 

  12. Drǎgan, C.-C., Gardham, D., Manulis, M.: Hierarchical attribute-based signatures. In: Camenisch, J., Papadimitratos, P. (eds.) CANS 2018. LNCS, vol. 11124, pp. 213–234. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00434-7_11

    Chapter  Google Scholar 

  13. El Kaafarani, A., Ghadafi, E.: Attribute-based signatures with user-controlled linkability without random oracles. In: O’Neill, M. (ed.) IMACC 2017. LNCS, vol. 10655, pp. 161–184. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71045-7_9

    Chapter  Google Scholar 

  14. El Kaafarani, A., Ghadafi, E., Khader, D.: Decentralized traceable attribute-based signatures. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 327–348. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04852-9_17

    Chapter  Google Scholar 

  15. El Kaafarani, A., Katsumata, S.: Attribute-based signatures for unbounded circuits in the ROM and efficient instantiations from lattices. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10770, pp. 89–119. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_4

    Chapter  Google Scholar 

  16. Escala, A., Herranz, J., Morillo, P.: Revocable attribute-based signatures with adaptive security in the standard model. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 224–241. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21969-6_14

    Chapter  MATH  Google Scholar 

  17. Fuchsbauer, G., Pointcheval, D.: Anonymous proxy signatures. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 201–217. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85855-3_14

    Chapter  Google Scholar 

  18. Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gardham, D., Manulis, M.: Hierarchical attribute-based signatures: short keys and optimal signature length. Cryptology ePrint Archive, Report 2019/382 (2019). https://eprint.iacr.org/2019/382

  20. Ghadafi, E.: Stronger security notions for decentralized traceable attribute-based signatures and more efficient constructions. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 391–409. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16715-2_21

    Chapter  Google Scholar 

  21. Groth, J.: Homomorphic Trapdoor Commitments to Group Elements. Cryptology ePrint Archive, Report 2009/007 (2009)

    Google Scholar 

  22. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24

    Chapter  Google Scholar 

  23. Herranz, J.: Attribute-based signatures from RSA. TCS 527, 73–82 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  24. Jager, T., Rupp, A.: The semi-generic group model and applications to pairing-based cryptography. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 539–556. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_31

    Chapter  Google Scholar 

  25. Kaaniche, N., Laurent, M., Rocher, P.-O., Kiennert, C., Garcia-Alfaro, J.: PCS, a privacy-preserving certification scheme. In: Data Privacy Management, Cryptocurrencies and Blockchain Technology, pp. 239–256 (2017)

    Google Scholar 

  26. Kakvi, S.A.: Efficient fully anonymous group signatures based on the Groth group signature scheme. Master’s thesis, University College London (2010)

    Google Scholar 

  27. Khader, D., Chen, L., Davenport, J.H.: Certificate-free attribute authentication. In: Parker, M.G. (ed.) IMACC 2009. LNCS, vol. 5921, pp. 301–325. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10868-6_18

    Chapter  Google Scholar 

  28. Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_30

    Chapter  Google Scholar 

  29. Krzywiecki, Ł., Sulkowska, M., Zagórski, F.: Hierarchical ring signatures revisited – unconditionally and perfectly anonymous schnorr version. In: Chakraborty, R.S., Schwabe, P., Solworth, J. (eds.) SPACE 2015. LNCS, vol. 9354, pp. 329–346. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24126-5_19

    Chapter  Google Scholar 

  30. Li, J., Au, M.H., Susilo, W., Xie, D., Ren, K.: Attribute-based signature and its applications. In: ACM ASIACCS 2010, pp. 60–69. ACM (2010)

    Google Scholar 

  31. Maji, H.K., Prabhakaran, M., Rosulek, M.: Attribute-based signatures. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 376–392. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19074-2_24

    Chapter  Google Scholar 

  32. Okamoto, T., Takashima, K.: Decentralized attribute-based signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 125–142. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_9

    Chapter  Google Scholar 

  33. Okamoto, T., Takashima, K.: Efficient attribute-based signatures for non-monotone predicates in the standard model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 35–52. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_3

    Chapter  Google Scholar 

  34. Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_32

    Chapter  Google Scholar 

  35. Sakai, Y.: Practical attribute-based signature schemes for circuits from bilinear map. IET Inf. Secur. 12, 184–193 (2018)

    Article  Google Scholar 

  36. Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_18

    Chapter  Google Scholar 

  37. Trolin, M., Wikström, D.: Hierarchical group signatures. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 446–458. Springer, Heidelberg (2005). https://doi.org/10.1007/11523468_37

    Chapter  Google Scholar 

  38. Tsabary, R.: An equivalence between attribute-based signatures and homomorphic signatures, and new constructions for both. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 489–518. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_16

    Chapter  Google Scholar 

Download references

Acknowledgements

Daniel Gardham was supported by the UK Government PhD studentship scheme. Mark Manulis was supported by the EPSRC project TAPESTRY (EP/N02799X). The authors thank the anonymous reviewers of ACNS 2019 for their valuable comments.

Author information

Authors and Affiliations

  1. Surrey Centre for Cyber Security, University of Surrey, Guildford, UK

    Daniel Gardham & Mark Manulis

Authors
  1. Daniel Gardham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Manulis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Gardham .

Editor information

Editors and Affiliations

  1. Singapore Management University, Singapore, Singapore

    Robert H. Deng

  2. Universidad del Rosario, Bogota, Colombia

    Valérie Gauthier-Umaña

  3. Cyxtera Technologies, Bogota, Colombia

    Martín Ochoa

  4. Columbia University, New York, NY, USA

    Moti Yung

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gardham, D., Manulis, M. (2019). Hierarchical Attribute-Based Signatures: Short Keys and Optimal Signature Length. In: Deng, R., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2019. Lecture Notes in Computer Science(), vol 11464. Springer, Cham. https://doi.org/10.1007/978-3-030-21568-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-21568-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21567-5

  • Online ISBN: 978-3-030-21568-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation